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Photons - class-XI

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The photoelectric cut off voltage in a certain experiment is 1.5 V. The maximum kinetic energy of photoelectrons emitted is then

  1. 2.4 eV

  2. 1.5 eV

  3. 3.1 eV

  4. 4.5 eV


Correct Option: B
Explanation:

The minimum negative potential applied to the plate or anode  for which the photoelectric current just becomes zero, So, in this case, maximum K.E of an electron will be equal to stopping potential.
Here, $V _0 \, = \, 1.5 \, V,$
Maximum Kinetic energy = $eV _{0} \, = \, 1.5 \,eV$

Light of wavelength 0.6 mm from a sodium lamp falls on a photocell and causes the emission of photoelectrons for which the stopping potential is 0.5 V. With light of wavelength 0.4 mm from a sodium lamp, the stopping potential is 1.5 V. With this data, the value of h/e is:

  1. $6\times {{10}^{-5}}\,V{{s}^{-1}} $

  2. $2\times {{10}^{-15}}\,V{{s}^{-1}} $

  3. $4\times {{10}^{-55}}\,V{{s}^{-1}} $

  4. $4\times {{10}^{-15}}\,V{{s}^{-1}} $


Correct Option: D
Explanation:

In emission of electron, Potential Energy

$eV = \dfrac{hc}{\lambda} - W _0$

When light of wavelength $\lambda =0.6\,mm$and stopping potential $0.5\,V$
$0.5e=\dfrac{hc}{6\times {{10}^{-7}}}-{{W} _{0}}\ ......\ (1)$

When light of wavelength $\lambda =0.4\,mm$and stopping potential $1.5\,V$
$1.5e=\dfrac{hc}{4\times {{10}^{-7}}}-{{W} _{0}}\ ......\ (2)$
subtract equation (1) from (2) $ e=\dfrac{hc}{{{10}^{-7}}}\left[ \dfrac{1}{4}-\dfrac{1}{6} \right] $

$ \Rightarrow \dfrac{h}{e}=\dfrac{12\times {{10}^{-7}}}{3\times {{10}^{8}}}=4\times {{10}^{-15}}\,V{{s}^{-1}} $ 

Photons absorbed in meter are converted to heat. A source emitting $n$ photons/s of frequency $v$ is used to convert $1\ kg$ of ice of ${0}^{o}c$ to water at ${0}^{o}C$. Then, the time taken for the conversion:

  1. decreases with increasing $n$, with $v$ fixed

  2. decreases with $n$ fixed, $v$ increasing

  3. remains constant with $n$ and $v$ changing such that $nv=$constant

  4. increases when the product $nv$ increases


Correct Option: A

The energy od proton in a light of wavelength 6000 $\mathring { A } $ is :
$(h = 6.63 \times 10^{-34}$ $Js,$ $c = 3 \times 10^8 m/s)$

  1. $6.81 \times 10^{-19} J$

  2. $5.61 \times 10^{-19} J$

  3. $3.31 \times 10^{-19} J$

  4. $2.31 \times 10^{-19} J$


Correct Option: C
Explanation:

$E = {{hc} \over \alpha }$

$ = {{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}} \over {6000 \times {{10}^{ - 10}}}}$

$ = 3.31 \times {10^{ - 19}}J$

A photo-electric threshold wavelength of tungsten is $2300 \mathring{A}$ . The energy of electrons ejected from the surface, if ultra -violet light of wavelength $1800 \mathring{A}$ is incident on it, is 

  1. 1.5 eV

  2. 2 eV

  3. 3.2 eV

  4. 6 eV


Correct Option: C

Calculate the kinetic energy of the electron having wavelength 1 nm

  1. 2.1 eV

  2. 3.1 eV

  3. 1.5 eV

  4. 4.2 eV


Correct Option: C

A laser beam ($\iota = 633\ nm$)has an power of $3mW$. What will be the pressure exerted on a surface by this beam if the cross sectional area is $3\ mm^{2}$ (Assume perfect reflection and normal incidence)

  1. $6.6\times 10^{-3}N/m^{2}$

  2. $6.6\times 10^{-6}N/m^{2}$

  3. $6.6\times 10^{-9}N/m^{2}$

  4. $6.6\ N/m^{2}$


Correct Option: B

A metalic surface is irradiated with monochr matic light of variable wavelength. Above wavelength of $ 5000 \dot { A }  $ , no photoelectrons a emitted from the surface. With an unknown wavelength, a stopping potential of 3V is nessary to eliminate the photo current . The Known wavelength is:

  1. 2258 $ \dot { A } $

  2. $ 4133 \dot { A } $

  3. $ 3126 \dot { A } $

  4. $ 2679 \dot { A } $


Correct Option: A

Two free protons are separated by a distance of $1\mathring A $. If they are released the kinetic energy of proton when it infinite separation is

  1. $23 \times 10 ^ { 19 } j$

  2. $11.5 \times 10 ^ { - 19 } \mathrm { J }$

  3. $46 \times 10 ^ { - 19 } \mathrm { J }$

  4. $5.6 \times 10$


Correct Option: B

The maximum energy of emitted photo electrons is measured by

  1. The current they produce

  2. The potential difference they produce

  3. The largest potential difference they can traverse

  4. The speed with which they emerge


Correct Option: C
Explanation:

Maximum energy of emitted photo electrons is equal to the stopping potential. Stopping potential is the largest potential difference an emitted photo electron can traverse.

If the work function of the metal is W and the frequency of the incident light is v , then there is no emission of photo-electrons if

  1. $v< W/h$

  2. $v > W/h$

  3. $v \geq W/h$

  4. $v \leq W/h$


Correct Option: A
Explanation:

Maximum Kinetic Energy $=h\nu -\phi $
$=h\nu -W $
Since there is no emission
So, $h\nu -W < 0$
or $\nu < \dfrac{W}{h}$

A proton, an electron and an $\alpha$ particle is accelerated through the same potential difference enter a region of uniform magnetic field, moving at right angles to the magnetic field $\vec{B}$. The ratio of their kinetic energies is

  1. 2:1:1

  2. 2:2;1

  3. 1:2:1

  4. 1:1:2


Correct Option: D
Explanation:

Kinetic energy = qV where q is charge and V is potential
But potential is same
So, $K. E \propto q$
$q _p = q _e = 2q$
Putting these values,
we get the ratio of 1:1 :2

Identify which of the following statement is true about the momentum of a photon?

  1. It is proportional to the wavelength of the photon

  2. It is inversely proportional to the wavelength of the photon.

  3. It is inversely proportional to the square of the wavelength of the photon.

  4. It is proportional to the mass of the photon.

  5. It is equal to the energy of the photon.


Correct Option: B
Explanation:

Momentum of the photon $p = \dfrac{h}{\lambda}$ where $\lambda$ is the wavelength of the photon

$\implies$$p  \propto \dfrac{1}{\lambda}$
Hence momentum of the photon is inversely proportional to the wavelength of the photon.

What should be the velocity of an electron so that its momentum becomes equal to that of a photon of wavelength $5200\overset {\circ}{A}$?

  1. $700\ m/s$

  2. $1000\ m/s$

  3. $1400\ m/s$

  4. $2800\ m/s$


Correct Option: C
Explanation:

Momentum, $p = mv = \dfrac {h}{\lambda}$


or $v = \dfrac {h}{m\lambda}$

$\therefore v = \dfrac {6.62\times 10^{-34}}{9.1\times 10^{-31}\times 5.2\times 10^{-7}}$

$\Rightarrow v = \dfrac {6.2\times 10^{4}}{9.1\times 5.1}$

$\Rightarrow v = 1400\ m/s$.

Ultraviolet radiation of 6.2 eV falls on an aluminium surface (work function 4.2 eV). The kinetic energy (in joule) of the fastest electron emitted is :

  1. $3.2 \times 10^{-21}$

  2. $1.6 \times 10^{-17}$

  3. $3.2 \times 10^{-19}$

  4. $3.2 \times 10^{-15}$


Correct Option: C
Explanation:

$Energy\quad of\quad radiation,\quad h\nu =6.2eV\ =6.2\times 1.6\times { 10 }^{ -19 }J\ Work\quad function\quad W=4.2eV\ =4.2\times 1.6\times { 10 }^{ -19 }J\ KE=h\nu -W\ =6.2\times 1.6\times { 10 }^{ -19 }-4.2\times 1.6\times { 10 }^{ -19 }\ =2\times 1.6\times { 10 }^{ -19 }\ =3.2{ \times 10 }^{ -19 }J$

Momentum of a photon having frequency $1.5\times 10^{13}Hz$?

  1. $3.13\times 10^{-29}kg m/s$

  2. $3.3\times 10^{-34}kg m/s$

  3. $6.6\times 10^{-34}kg m/s$

  4. $6.6\times 10^{-30}kg m/s$


Correct Option: A
Explanation:

$\quad Momentum\quad of\quad a\quad photon\quad is\quad P=\quad h/\lambda \ \quad And\quad \quad \quad \lambda \nu =c\quad ,\quad where\quad c=\quad speed\quad of\quad light\quad h=\quad Planck's\quad constant\ \qquad \qquad \qquad \qquad \qquad \qquad \lambda =\quad wavelength\quad of\quad photon\ \qquad \qquad \qquad \qquad \qquad \qquad \nu =\quad frequency\quad of\quad photon\ so\quad \lambda =\quad \dfrac { 3\times { 10 }^{ 8 } }{ 1.5\times { 10 }^{ 13 } } =2\times { 10 }^{ -5 }{ m }^{ }\quad P=\dfrac { 6.26\times { 10 }^{ -34 } }{ 2\times { 10 }^{ -5 } } =3.13\times { 10 }^{ -29 }kg m/s\ Therefore\quad option\quad A.\quad$

A beam of light has two wavelengths $4971\mathring{A}$ and $6216\mathring{A}$ with a total intensity of $3.6\times { 10 }^{ -3 }W{ m }^{ -2 }$ equally distributed among the two wavelengths. The beam falls normally on an area of $1{cm}^{2}$ of a clean metallic surface of work function $2.3eV$. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photo electrons liberated in $2s$ approximately :

  1. $6\times { 10 }^{ 11 }$

  2. $9\times { 10 }^{ 11 }$

  3. $11\times { 10 }^{ 11 }$

  4. $15\times { 10 }^{ 11 }$


Correct Option: B
Explanation:
${ E } _{ 1 }=\cfrac { 1242 }{ 497.2 } =2.50eV;{ E } _{ 2 }=\cfrac { 1242 }{ 6621. } =2.0eV$
so, photoelectron emission takes place only due to first wavelength
$\therefore$ No. of photoelectrons emitted $=\cfrac { 1.8\times { 10 }^{ -3 }\times { 10 }^{ -4 }\times 2 }{ 2.5\times 1.6\times 10^{-19} } hv=9\times { 10 }^{ 11 }$

The threshold frequency for a metallic surface corresponds to an energy of $6.2eV$, and the stopping potential for a radiation incident on this surface $5V$. The incident radiation lies in.

  1. X-ray

  2. ultra-violet region

  3. infra-red region

  4. visible region


Correct Option: B
Explanation:

$hv=5eV+6.2eV=11.2eV$
$\lambda =\cfrac { 1242 }{ 11.2 } nm=1109\mathring { A } $
it lies in ultraviolet region

When photon of the energy 3.8 eV falls on metallic surface of work function 2.8 eV, then the kinetic energy of emitted electrons are

  1. 1 eV

  2. 6.6 eV

  3. 0 to 1 eV

  4. 2.8 eV


Correct Option: A
Explanation:

Photoelectric law

$KE=h\nu -W\ h\nu =3.8eV\ W=2.8eV\ KE=3.8-2.8\ =1eV$

An electron of mass $m$ and charge $e$ is accelerated from rest through a potential difference of $V$ volt in vacuum. Its final speed will be

  1. $\cfrac { eV }{ 2m } $

  2. $\cfrac { eV }{ m } $

  3. $\sqrt { \cfrac { 2eV }{ m } } $

  4. $\sqrt { \cfrac { eV }{ 2m } } $


Correct Option: C
Explanation:
  • Energy gained by electron when accelerated through a potential $V $ is $ charge\times voltage$ i.e., $eV$ 
  • As Kinetic energy 
  •  of any mass $m$ is given as $\dfrac{mv^2}{2}$ 
  • so velocity $v$= $\sqrt[2]{ \dfrac{2K.E.}{m}}$ 
  • for final speed put $K.E.= eV$ we get final speed $v$= $ \sqrt[2]{ \dfrac {2eV}{m}}$. Option C is correct

A hydrogen-like atom is in a higher energy level of quantum number $6$. The excited atom make a transition to first excited state by emitting photons of total energy $27.2\ eV$. The atom from the same excited state make a transition to the second excited state by successively emitting two photons. If the energy of one photon is $4.25\ eV$, find the energy of other photon.

  1. $5.25\ eV$

  2. $6.25\ eV$

  3. $6.95\ eV$

  4. $7.80\ eV$


Correct Option: A
Explanation:
Total energy liberated during transition of ${ e }^{ - }$ from ${ n }^{ th }$ shell to first excited state
i.e, ${ 2 }^{ nd }$ shell $=10.20+17.0=2720eV$
                     $=27.20\times 1.602\times { 10 }^{ -12 }erg$
$\dfrac { hc }{ \lambda  } ={ R } _{ H }\times { Z }^{ 2 }{ h } _{ c }\left[ \dfrac { 1 }{ { z }^{ 2 } } -\dfrac { 1 }{ { n }^{ 2 } }  \right] $
$27.20\times 1.602\times { 10 }^{ -12 }={ R } _{ H }\times { Z }^{ 2 }{ h } _{ c }\left[ \dfrac { 1 }{ { z }^{ 2 } } -\dfrac { 1 }{ { n }^{ 2 } }  \right] \quad \longrightarrow \left( 1 \right) $
i.e. ${ 3 }^{ rd }$ shell $=4.25+5.95=10.20eV$
                     $=10.20\times 1.602\times { 10 }^{ -12 }erg$
$\therefore$   $10.20\times 1.602\times { 10 }^{ -12 }={ R } _{ H }\times { Z }^{ 2 }{ h } _{ c }\left[ \dfrac { 1 }{ { 3 }^{ 2 } } -\dfrac { 1 }{ { n }^{ 2 } }  \right] $ $\longrightarrow \left( 2 \right) $
We get $n=5.25eV$

Calculate the number of photons emitted per seconds from a monochromatic light source of $40\ W$, giving out light of wavelength $5000\ \mathring {A}$.

  1. $1.0\ \times  10^{30}$

  2. $1.0\ \times  10^{20}$

  3. $1.0\ \times  10^{10}$

  4. $1.0\ \times  10^{25}$


Correct Option: B

In a photoelectric cell, illuminated with a certain radiation, the minimum negative anode of potential with respect to emitting metal required to stop the electron is $2 V.$ the  minimum KE of the photoelectrons is 

  1. $0 eV$

  2. $1 eV$

  3. $2 eV$

  4. $ 4 eV$


Correct Option: C
Explanation:

Given,

$V _0=2V$
The minimum kinetic energy of the photo electron is
$K _{min}=eV _0$
$K _{min}=2eV$
The correct option is C.

The difference in the electron energies associated wiwth the two state of an atom is $4 eV$. if $\frac { h }{ e } =4\times { 10 }^{ -5 }{ JsC }^{ -1 }$, the wavelength of the photon emitted as a result of the above transition will be

  1. $6000 A$

  2. $3000 A$

  3. $1000 A$

  4. $9000 A$


Correct Option: A

When a hydrogen atom emits a photon of energy $12.09eV$,it's orbit's angular momentum changes by (where $h$ is Planck's constant) ?

  1. $\dfrac{3h}{\pi}$

  2. $\dfrac{2h}{\pi}$

  3. $\dfrac{h}{\pi}$

  4. $\dfrac{4h}{\pi}$


Correct Option: C
Explanation:

Given that,

Emission of photon of 12.1eV corresponds to the transition from

$n=3,n=1$

Now, change in angular momentum

  $ =\left( {{n} _{2}}-{{n} _{1}} \right)\times \dfrac{h}{2\pi } $

 $ =\left( 3-1 \right)\times \dfrac{h}{2\pi } $

 $ =\dfrac{h}{\pi } $

Hence, this is the required solution 

Assuming photo-emission to take place, the factor by which the maximum velocity of the emitted photo electrons changes when the wavelength of the incident radiation is increased four times, is (assuming work function to be negligible in comparison to $hcl\lambda $)

  1. 4

  2. $\dfrac{1}{4}$

  3. 2

  4. $\dfrac{1}{2}$


Correct Option: D
Explanation:

Einstein's Photoelectric equation is given as : $\dfrac{hc}{\lambda } = \phi + \dfrac{1}{2} mv^{2}$ (where $\phi $ = work function , v = velocity of photoelectron, $\lambda $ = wavelength of incident radiation) 

 as $\dfrac{hc}{\lambda } >>\phi \Rightarrow \dfrac{hc}{\lambda }\approx \dfrac{1}{2} mv^{2}$

 now wavelength is increased by 4 times : 

 $\Rightarrow \lambda _{2}=4\lambda $ 

 $\Rightarrow \dfrac{hc}{4\lambda }=\dfrac{1}{2} mv _{2}^{2}$

 $\Rightarrow \dfrac{1}{4}\left ( \dfrac{1}{2} mv^{2}\right )=\dfrac{1}{2}mv _{2}^{2}$ 

 $v _{2}^{2}=\dfrac{v^{2}}{4}\Rightarrow v _{2}=\dfrac{v}{2}$ 

 so maximum velocity of photoelectrons will be $\dfrac{1}{2}$ times when wavelength becomes 4 times.

Momentum of $\gamma-ray$ photon of energy $3\ keV$ in $kg-m/s$ will be

  1. $2.95 \times 10^{-23}$
  2. $1.6\times 10^{-21}$

  3. $1.6\times 10^{-24}$

  4. $1.6\times 10^{-27}$


Correct Option: A
Explanation:

If the energy of the electron is $E=3KeV=3\times 10^3 eV=3\times 1.6\times 10^{-16}Joule$

 
Then the momentum ,$p$ is given by  $p=\sqrt[2]{2mE}=\sqrt[2]{2\times 9.1\times 10^{-31} \times 4.8\times 10^{-16}}=2.95\times 10^{-23} Kgm/s$
Where $m=9.1\times 10^{-31}Kg$ is mass of electron.

Radiational wave length $ \lambda $=124 nm falls on a metallic surface. Then the kinetic energy of the ejected photo electron(s) can be : (Given that threshold wavelength ($ \lambda _{0} $)=248 nm)

  1. 1 eV

  2. 2 eV

  3. 3 eV

  4. 5 eV


Correct Option: D
Explanation:
We know,
$KE=hv-h{ v } _{ 0 }$
        $=hc\left[ \dfrac { 1 }{ \lambda  } -\dfrac { 1 }{ { \lambda  } _{ 0 } }  \right] $
$=6.626\times { 10 }^{ -34 }\times 3\times { 10 }^{ 8 }\times \left[ \dfrac { 1 }{ 124\times { 10 }^{ -9 } } -\dfrac { 1 }{ 248\times { 10 }^{ -9 } }  \right] $
$=0.08015\times { 10 }^{ -17 }$
$=8.015\times { 10 }^{ -19 }J$
$1.6\times { 10 }^{ -19 }J=1eV$
$8.015\times { 10 }^{ -19 }J=\dfrac { 1 }{ 1.6\times { 10 }^{ -19 } } \times 8.015\times { 10 }^{ -19 }$
                            $=4.74eV$
Thus, the answer is close to $5eV$.

Total energy of $electron$ is more than energy of $photon$ if both are having $equal\ \lambda.$

  1. True

  2. False


Correct Option: A

Monochromatic light of wavelength 440 nm is produced. The power emitted by light is 18 mW, The number of photons emitted per second by light beam is :

$(h=6.6\times { 10 }^{ -34 })$

  1. $2.09\times { 10 }^{ 16 }$

  2. $4\times { 10 }^{ 16 }$

  3. $3\times { 10 }^{ 18 }$

  4. $4\times { 10 }^{ 18 }$


Correct Option: B
Explanation:

Given,


$\lambda=440nm$


$h=6.6\times 10^{-34}$

$I=18m W$

The energy of monochromatic light,

$E=\dfrac{hc}{\lambda}$

$E=\dfrac{6.6\times 10^{-34}\times 3\times 10^8}{440\times 10^{-9}}$

$E=0.045\times 10^{-17}J$

The number of photon emitted per second by the light beam,

$n=\dfrac{I}{E}$ 

$n=\dfrac{18\times 10^{-3}}{0.045\times 10^{-17}}$

$n=4\times 10^{16}$

The correct option is B.

An electron of stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be

  1. $\dfrac{25m}{24hR}$

  2. $\dfrac{24m}{25hR}$

  3. $\dfrac{24hR}{25m}$

  4. $\dfrac{25hR}{24m}$


Correct Option: C

Violet light is falling on a photosensitive material causing ejection of photoelectrons with maximum kinetic energy of $1$ eV. Red light falling on metal will cause emission of photoelectrons with maximum kinetic energy (approximately) equal to

  1. $1.2$ eV

  2. $0.9$ eV

  3. $0.5$ eV

  4. Zero, that is no photoemision


Correct Option: D

When an electron de-exited back from ${\left( {n + 1} \right)^{th}}$ state to ${n^{th}}$ state in a hydrogen like atoms, wavelength of radiations emitted is ${\lambda _1}\left( {n >  > 1} \right)$. In the same atom de-broglies wavelength associated with an electron in $nth$ state is ${\lambda _2}$. Then $\frac{{{\lambda _1}}}{{{\lambda _2}}}$ is proportional to 

  1. $\frac{1}{n}$

  2. n

  3. ${n^2}$

  4. ${n^3}$


Correct Option: A

Approximately, the temperature corresponding to $1 eV$ translational kinetic energy of molecule is

  1. $7.6 \times 10 ^ { 2 } \mathrm { K }$

  2. $7.7 \times 10 ^ { 3 } \mathrm { K }$

  3. $7.1 \times 10 ^ { - 2 } \mathrm { K }$

  4. $7.2 \times 10 ^ { 3 } \mathrm { K }$


Correct Option: B

The work function of a metal is $3.3\times{  10}^{  -19}J$. The maximum wavelength of the photons required to eject electron from the metal is:

  1. $200nm$

  2. $300nm$

  3. $400nm$

  4. $600nm$


Correct Option: A

A metal plate of area $1\times { 10 }^{ -4 }{ m }^{ 2 }$ is  illuminated by a radiation of intensity 16 m $W/{ m }^{ 2 }.$ The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be :
$\left[ { 1eV=1.6\times 10^{ 19 }J } \right] $

  1. ${ 10 }^{ 12 } and\ 5eV$

  2. ${ 10 }^{ 11 } and\ 2.5eV$

  3. ${ 10 }^{ 10 } and\ 5eV$

  4. ${ 10 }^{ 14 } and\ 5eV$


Correct Option: A

The energy of a hydrogen-like atom (or ion ) in its ground state is - 122.4 eV. It may be :

  1. hydrogen atom

  2. $He^{+}$

  3. $Li^{2+}$

  4. $Be^{3+}$


Correct Option: C

When radiations of wavelength 3000 are incident on a photosensitive surface, the kinetic energy of electrons is 2.5 eV. The stopping potential for 1500 will he,

  1. $V _ { s } = 2.5 \mathrm { V }$

  2. $V _ { s } = 5.0 \mathrm { V }$

  3. $2.5 \leq \mathrm { V } _ { \mathrm { s } } \leq 5.0 \mathrm { V }$

  4. $V _ { s } > 5.0 \mathrm { V }$


Correct Option: D

A photon of energy 12.75 eV is completely absorbed by a hydrogen atom initially in the ground state. The quantum number of the excited state is:

  1. $2$

  2. $3$

  3. $4$

  4. $5$


Correct Option: C

If an $\alpha$-particle is accelerated with the potential V, the energy of $\alpha$-particle will be 

  1. 1 eV

  2. 2 eV

  3. 3 eV

  4. 4 eV


Correct Option: B

If an $\alpha$-particle and a proton are accelerated from rest by a potential difference of 1 megavolt then the ratio of their kinetic energy will be

  1. 1:1

  2. 2:1

  3. 1:2

  4. 1:4


Correct Option: A

A photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $\cfrac{\lambda}{2}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is $3$ times that in the first case, the work function of the surface of the material is  ($h=$ Planks constant, $c=$ speed of light)

  1. $\cfrac{hc}{3\lambda}$

  2. $\cfrac{hc}{2\lambda}$

  3. $\cfrac{hc}{\lambda}$

  4. $\cfrac{2hc}{\lambda}$


Correct Option: B

In photoelectric effect for silver threshold is $\lambda _0 = 3250 \times 10^{-10} m$. If U.V of $\lambda = 2536 \times 10^{-10}$ is incident then velocity of electron from will be 

  1. $6 \times 10^6$

  2. $3 \times 10^6$

  3. $6 \times 10^5$

  4. $3 \times 10^5$


Correct Option: C

Find the maximum $KE$ of photoelectrons emitted from the surface of lithium$(\phi=2.39 eV)$ when exposed with $\displaystyle E=E _{0}(1+\cos 6\times10^{14}t)\cos 3.6\times 10^{15}t$

  1. 0.37 $eV$

  2. 0.1 $eV$

  3. 0.02 $eV$

  4. 0.06 $eV$


Correct Option: C
Explanation:

For maximum $KE.$ frequency should be maximum. Here,
$\displaystyle w=3.6\times10^{15}s^{-1}$


$\displaystyle (KE) _{max}=\dfrac{hw}{2\pi}-\phi$

$=\displaystyle =\dfrac{6.625\times10^{-34}\times3.6\times10^{+15}}{6.28\times1.6\times10^{-19}}-2.39$

$=2.36-2.39$
$=0.02$ $eV$
So, the answer is option (C).

Two separate monochromatic light beams A and B of the same intensity are falling normally on a unit area of a metallic surface. Their wavelengths are $\lambda _A$ and $\lambda _B$, respectively. Assuming that all the incident light is used in ejecting the photoelectrons, the ratio of the number of photoelectrons from beam A to that from B is

  1. $(\lambda _A/ \lambda _B)^2$

  2. $\lambda _A/ \lambda _B$

  3. $\lambda _B/ \lambda _A$

  4. 1


Correct Option: B

The momentum of a photon of energy 1MeV, in kg/m/s, will be :

  1. $\displaystyle 10^{-22}$

  2. $\displaystyle 0.33\times 10^{6}$

  3. $\displaystyle 5\times 10^{-22}$

  4. $\displaystyle 7\times 10^{-24}$


Correct Option: C
Explanation:

The momentum of photon is given by


$p = \dfrac{E}{c}$

where, E is the energy of photon(in eV) and c is the velocity of light , $c = 3 \times 10^8 ms^{-1}$.

$p = \dfrac{1 \times 10^{6} \times 1.6 \times 10^{-19}}{3 \times 10^8}$


$p =  0.533 \times 10^{-21}$

$p = 5 \times 10^{-22} kgsm^{-1}$

So, the answer is option (C).

When light is made incident on a surface, then photoelectrons are emitted from it. The kinetic energy of photoelectrons

  1. Depends on the wavelength of incident light

  2. Is same

  3. Is more than a certain minimum value

  4. None of these


Correct Option: A
Explanation:

The photoelectric effect related with the incident light frequency $(\nu)$ by the following equation:
$E _k=eV _s=h\nu-\phi$,
where, $\phi$ is the work function of the material and $E _k$ is the kinetic energy of the photo electron. So the photoelectrons emitted from the surface of sodium metal are of speeds from zero to a certain maximum depending on the incident photon energy. So, the kinetic energy of photoelectrons depends on the wavelength of incident light.

So, the answer is option (A).

The work function of aluminum is 4.2eV. Light of wavelength $\displaystyle 2000\mathring {A} $ is incident on it. The maximum energy of emitted electrons will be

  1. Zero

  2. 1.99 volt

  3. 3.2 volt

  4. 6.19 volt


Correct Option: B
Explanation:

The work function of aluminium is
$\phi = 4.2 eV = 4.2 \times 1.6 \times 10^{-19}$
$\phi = 6.72 \times 10^{-19} J$
The energy of incident photon is

$h\nu = \dfrac{hc}{\lambda}$
$h\nu = \dfrac{6.6 \times 10^{-34} \times 3 \times 10^8}{2000\times 10^{-10}}$
$h\nu = 9.9 \times 10^{-19} J$
The maximum energy of photoelectrons is
$E _{max} = h\nu - \phi$
$E _{max} = 9.9 \times 10^{-19} - 6.72 \times 10^{-19}$
$E _{max} = 3.18 \times 10^{-19} J$
$E _{max} = \dfrac{3.18 \times 10^{-19}}{1.6 \times 10^{-19}}$
$E _{max} = 1.99 eV$
So, the answer is option (B).

The work function of aluminum is 4.2eV. Light of wavelength $\displaystyle 2000\mathring {A} $ is incident on it. The minimum energy of emitted electrons will be 

  1. Zero

  2. 2.0 eV

  3. 4.2 eV

  4. 6.19 eV


Correct Option: B
Explanation:

Energy of the incident light is $6.2 eV$. Now the work function of aluminum is $4.2$. So the  minimum energy of emitted electrons will be $(6.2-4.2)=2$ eV.

So, the answer is option (B).

The work function of a metal is X eV. When light of energy 2X is made incident on it then the maximum kinetic energy of emitted photoelectron will be 

  1. $2.5X \ eV$

  2. $2X \ eV$

  3. $X \ eV$

  4. $3X \ eV$


Correct Option: C
Explanation:

The maximum kinetic energy of emitted photoelectron is given as
$E _{max} = h\nu - \phi$
where,$\nu$ is the frequency of incident light and $\phi$ is photoelectric work function of metal. 
$E _{max} = 2X - X$ ...................(given)
$E _{max} = X \ eV$

So, the answer is option (C).

A 14 eV energy photon ionises a hydrogen atom in its lowest energy level. The kinetic energy of the electron ejected from the atom will be :

  1. 14 eV

  2. 13.6 eV

  3. 27.6 eV

  4. 0.4 eV


Correct Option: D

The threshold wavelength of a photosensitive metal is $662.5\ nm$. If this metal is irradiated with a radiation of wavelength $331.3\ nm$, find the maximum kinetic energy of the photoelectrons.

  1. 1.87 eV

  2. 18.7 eV

  3. 17.8 eV

  4. 1.78 eV


Correct Option: A

The wavelength of a photon is $5000\mathring {A} $.Its momentum will be:

  1. $1.32 \times 10^{-27 }kg\times$ meter/sec

  2. $1.5 \times 10^{-27 }kg\times$ meter/sec

  3. $2.32 \times 10^{-27 }kg\times$ meter/sec

  4. $5 \times 10^{-27 }kg\times$ meter/sec


Correct Option: A

Momentum of $ \gamma -ray $ photon of energy 3 KeV in kg-m/s will be 

  1. $ 1.6 \times 10^{-19} $

  2. $ 1.6 \times 10^{-2} $

  3. $ 1.6 \times 10^{-24} $

  4. $ 1.6 \times 10^{-27} $


Correct Option: C

What is the momentum of a photon having frequency $1.5 \times 10^{13} Hz $ 

  1. $3.3 \times 10 - 29\, kg\,m/s $

  2. $3.3 \times 10 - 34\, kg\, m/s$

  3. $6.6 \times 10 - 34\, kg\, m/s$

  4. $6.6 \times 10 - 30\, kg\, m/s$


Correct Option: A

The frequency and the intensity of a beam of light falling on the surface of a photoelectric material are increased by a factor of two. This will :

  1. Increase the maximum kinetic energy of the photoelectrons by 2 and photoelectric current by a factor of 1 / 2

  2. Increase the maximum kinetic energy of the photoelectrons, and increase the photoelectric current by a factor of 2

  3. Increase the maximum kinetic energy of the photoelectrons by a factor of 2 and will have no effect on the magnitude of the photoelectric current produced

  4. Not produced any effect on the kinetic energy of the emitted electrons but will increase the photoelectric current by a factor of 2


Correct Option: B
Explanation:

Doubling the frequency will double the kinetic energy of the photo electron.

Since kinetic energy (E) is given by:
$E=h\nu - \phi$, where $\phi$ is the work function of the material. 
Again the intensity of the light means the increase of number of incident photon on the surface. This will increase the number of ejected photon from the surface in proportionate manner.

The frequency of incident light falling on a photosensitive metal plate is doubled, the KE of the emitted photoelectrons is

  1. Double the earlier value

  2. Unchanged

  3. More then doubled

  4. Less than doubled


Correct Option: C
Explanation:

From Einstein's equation for photoelectric effect , the maximum kinetic energy , $K=h\nu-W$

where $\nu=$ frequency of incident light , $h=$ Planck's constant and $W=$ work function of metal. 
When $\nu$ is made double, $K'=2h\nu-W=2(h\nu-W)+W=2K+W$  
Thus, kinetic energy of photoelectrons will be more than doubled when incident frequency is doubled.  

When orange light falls on a photo sensitive surface the photocurrent begins to flow.Velocity of emitted electrons will be more when surface is hit by

  1. Red light

  2. Violet light

  3. Thermal radiations

  4. Radio waves


Correct Option: B
Explanation:

Frequency of Red light, thermal radiations and radio waves and less than frequency of orange light whereas frequency of violet light is more than frequency of orange light. So, violet light has more energy.

Since energy $=h\nu $
So, when violet light is hit on the surface velocity of emitted electrons will be more.

Assertion (A) : For a fixed incident photon energy, photoelectrons have a wide range of energies ranging from zero to the maximum value $K _{max}$
Reason (R) : Initially, the electrons in the metal are at different energy level.

  1. Both A and R are true and R is the correct explanation of A

  2. Both A and R are true but R is not the correct explanation of A

  3. A is true but R is false

  4. A is false but R is true


Correct Option: A
Explanation:

Photoelectrons have energy range from zero to the maximum kinetic energy because electrons in the metal have different energy in different energy level.

When light falls on a photosensitive surface, electrons are emitted from the surface. The kinetic energy of these electrons does not depend on the:

  1. Wave length of light

  2. Frequency of light

  3. Type of material used for the surface

  4. Intensity of light.


Correct Option: D
Explanation:

Kinetic energy of photo electrons depend on the wavelength of light, frequency of light, work function of metal, which is property of material, and thickness of the surface layer. Whereas it is independent of intensity of light.

The photoelectrons emitted from a metal surface are such that their velocity

  1. Is zero for all

  2. Is same for all

  3. Lies between zero and infinity

  4. Lies between zero and a finite maximum


Correct Option: D
Explanation:

Suppose radiation of energy $E + \phi$ is incident on a metal surface
$\phi$ is the work function and is the energy need to eject a photoelectron..
Assume all of E gets converted to Kinetic energy.


$E = \dfrac{1}{2}mv^{2}$ 

Hence, $v = \sqrt{\dfrac{2E}{m}}$

There would be molecules that absorb energy lying from $0$ to $E$.
And hence their velocities would lie between $0$ and $v$.

The photoelectric threshold of Tungsten is 2300$ \mathring {A }$. The energy of the electrons ejected from the surface by ultraviolet light of wavelength 18000 $ \mathring {A }$ is 

  1. 0.15 e V

  2. 1.5 e V

  3. 15 e V

  4. 150 e V


Correct Option: A
Explanation:

$E _k=d\dfrac{h}{c}\left ( \dfrac{1}{\lambda } -\dfrac{1}{\lambda _o}\right )(in \, e\, V)$

$=\dfrac{6.6\times 10^{34}\times 3\times 10^8}{1.6 \times 10^{-19}}$$\left ( \dfrac{10^{10}}{1800}-\dfrac{10^{10}}{2300} \right )=0.15 e V$

When light is incident on a metal surface the maximum kinetic energy of emitted electrons

  1. Vary with intensity of light

  2. Vary with frequency of light

  3. Vary with speed of light

  4. Vary irregulary


Correct Option: B
Explanation:

Photoelectric effect
$KE _{max} = hv - W _o$
where,$W _o$ is the work function of the metal
Clearly $KE$ varies linearly with the the frequency of the photons.

Ultraviolet radiation of 6.2eV falls on an aluminium surface (work function 4.2eV). The kinetic energy in joule of the faster electron emitted is approximately

  1. $3.2\times 10^{21}$

  2. $3.2\times 10^{-19}$

  3. $3.2\times 10^{-17}$

  4. $3.2\times 10^{-15}$


Correct Option: B
Explanation:

$E _k=E-W _o=6.2-4.2=2.0 e V$
$=2.0 \times 1.6 \times 10^{-19}=3.2\times 10^{-19}\, J$

The ratio of de-Broglie wavelengths of proton and $\alpha$-particle having same kinetic energy is

  1. $\sqrt2 :1$

  2. $2\sqrt2 :1$

  3. 2 :1

  4. 4 : 1


Correct Option: C
Explanation:

De Broglie wavelength is given by:


$\lambda = \dfrac{h}{p}$ 

Writing momentum as a a function of kinetic energy and mass

$\lambda = \dfrac{h}{\sqrt{2Em}}$

i.e.   $\dfrac{\lambda _{proton}}{\lambda _{alpha}} = \sqrt{\dfrac{m _{alpha}}{m _{proton}}}$

$m _{alpha} = 4m _{proton}$
So,

$\dfrac{\lambda _{proton}}{\lambda _{alpha}} = \sqrt{\dfrac{m _{alpha}}{m _{proton}}} = \sqrt{\dfrac{4}{1}} = 2$

$K _{1} $and $K _{2}$ are the maximum kinetic energies of the photoelectrons emitted when light of wavelength $\lambda _{1} $ and $\lambda _{2} $  respectively are incident on a metallic surface. If $\lambda _{1}= $3$\lambda _{2} $  then

  1. $K _{1}>\dfrac{K _{2}}{3}$

  2. $K _{1}<\dfrac{K _{2}}{3}$

  3. $K _{1}=3K _{2}$

  4. $K _{2}=3K _{1}$


Correct Option: B
Explanation:

$K _{1}=\dfrac{hc}{\lambda _{1} }-\phi $-----------(1)

$K _{2}=\dfrac{hc}{\lambda _{2}}-\phi$-----------(2)

$\because\lambda _{1} = 3 \lambda _{2}$

$k _{2}=3\left(\dfrac{hc}{\lambda _{1}}\right)-\phi$---------(3)

$\dfrac{k _{2}}{3}=\dfrac{hc}{\lambda _{1}}-\dfrac{\phi}{3}$----------(4)

$\dfrac{k _{2}}{3}=(k _{1}+\phi)-\dfrac{\phi}{3}$  (by (1))

$\dfrac{k _{2}}{3}=k _{1}+\dfrac{2 \phi}{3}$

So,$k _{1}< \dfrac{k _{2}}{3}$

The work function of a metal is $1.6\times 10^{-19}$J. When the metal surface is illuminated by the light of wavelength 6400 $A^{o}$, then the maximum kinetic energy of emitted photoelectrons will be ($h = 6.4 \times 10^{-34} Js$)

  1. $14\times 10^{-19}J$

  2. $2.8\times 10^{-19}J$

  3. $1.4\times 10^{-19}J$

  4. $1.4\times 10^{-19}eV$


Correct Option: C
Explanation:

$K.E. _{max}=\dfrac{hc}{\lambda }-\phi $


$=\dfrac{6.4\times 10^{-34}\times 3\times 10^{8}}{6.4\times 10^{-7}}-1.6\times 10^{-19}$

$=3\times 10^{-19}-1.6\times 10^{-19}$
$=1.4\times 10^{-19}J.$
So, the answer is option (C).

The work function of a metal is 4.6eV. The wavelength of incident light required to emit photo-electrons of zero energy from its surface, will be

  1. 5000 $A^{0}$

  2. 3100 $A^{0}$

  3. 1700 $A^{0}$

  4. 2700 $A^{0}$


Correct Option: D
Explanation:
$E=\dfrac{hc}{\lambda}$

$ 4.6eV=\dfrac{1240eV}{\lambda}$

        $\lambda=2700{A}^{0}$

The photoelectric work function of a metal surface is 2eV. When light of frequency $1.5 \times10^{15}$ Hz is incident on it, maximum kinetic energy of the photo-electrons, approximately is :

  1. 8 eV

  2. 6 eV

  3. 2 eV

  4. 4 eV


Correct Option: D
Explanation:

$K.E. _{max}=h\nu-\phi $


=$\dfrac{6.6\times 10^{-34}\times 1.5\times 10^{15}}{1.6\times 10^{-19}}eV-2eV$

$=6eV-2eV$

$=4eV.$

So, the answer is option (D).

Work function of a metal is 3.0eV. It is illuminated by a light of wavelength $3 \times 10^{-7}$m. Then the maximum energy of the electron is.

  1. $2.34 \ eV$

  2. $0.85 \ eV$

  3. $1.13 \ eV$

  4. $3.32 \ eV$


Correct Option: C
Explanation:

$Maximum \ \ energy =\dfrac{hc}{\lambda}-\phi  (3\times 10^{-7}m=300nm)$

$=\dfrac{1240}{300} - 3 \ \ \ \ (hc =  1240 \ eV / X nm)$
$=4.13-3$
$=1.13 eV.$
So, the answer is option (C).

The energy of the incident photon is 12.38 eV, while the energy of the scattered photon is 9.4 eV. The K.E. of the recoil electron is nearly

  1. 2 eV

  2. 1 eV

  3. 4 eV

  4. 3 eV


Correct Option: D
Explanation:

K.E of the recoil electron
= energy of the incident photon - energy of scattered photon
= 12.38 eV -9.4eV
$\simeq 3eV.$

So, the answer is option (D).

Light of wavelength 5000 $A^{o}$ falls on a sensitive plate with photoelectric work function 1.9eV. The maximum kinetic energy of the photoelectrons emitted will be

  1. $0.58 \ eV$

  2. $2.48 \ eV$

  3. $1.24 \ eV$

  4. $1.16 \ eV$


Correct Option: A
Explanation:

$\lambda =5000 A^{0}  =  500nm$

$K.E. _{max} =\dfrac{hc}{\lambda }-\phi $

$=\dfrac{1240}{500}-1.9 \ \ \ \  (hc = 1240  eV - nm)$

$=2.48-1.9$
$=0.58 \ eV$
So, the answer is option (A).

When light of wavelength 2480 $A^{0}$ is incident on a metal surface electrons are emitted with a maximum KE of 2 eV. The maximum KE of photo-electrons, if light of wavelength 1240 $A^{0}$ is incident on the same surface would be

  1. 4eV

  2. 1 eV

  3. 2eV

  4. 7eV


Correct Option: D
Explanation:

From the 1st condition
$\dfrac{hC}{\lambda} - W = 2eV$

$h \ in \ terms \ of \ eV = \dfrac{6.63 \times 10^{-34}}{1.6 \times 10^{-19}}$

$\Rightarrow \dfrac{4.14 \times 10^{-15} \times 3 \times 10^{8} \times 10^{10}}{2480}$

$\Rightarrow Work for = \left ( 5.012 - 2 \right )eV$

$\Rightarrow W \approx 3eV$

So,
In 2nd case when wavelength of incident light is $1240 A^{\circ}$,
$\Rightarrow \dfrac{hC}{\lambda} - W = K. E.$

$\Rightarrow K. E. = \dfrac{4.14 \times 10^{-15} \times 3 \times 10^{18}}{1240} - 3$

$=10 - 3 = 7eV$

So, the answer is option (D).

The cut-off voltage in a photoelectric experiment is 3V. Then the maximum KE of photo-electrons emitted is

  1. 3 V

  2. 3 eV

  3. 6 eV

  4. 9 eV


Correct Option: B
Explanation:

Cut off voltage is the minimum voltage applied across the plates that even the electrons ejected with minimum kinetic energy could not reach the other plate.
So, 
From the definition,
Cut off voltage $= 3V$
Work done on the charge $=$ Kinetic energy of the photons
$\Rightarrow 3V \times 1e = K. E.$
$\Rightarrow K. E. = 3eV$

So, the answer is option (B).

If the frequency of light incident on a photosensitive metal plate is doubled, then the KE of photoelectrons will be

  1. Doubled

  2. Halved

  3. Quadrupled

  4. More than twice the previous value


Correct Option: D
Explanation:

$\ KE\ =\ h(V-V _{0})$
$\ V^{1}\ =\ 2V$
$\ KE^{1}\ =\ h(2V-V _{0})$
$\ KE^{1}\ =\ 2h(V-V _{0}) +\ hV _{0}$
$\ KE^{1}\ =\ 2KE+hV _{0}$

So, the answer is option (D).

The photo-electric threshold wavelength for a metal is $5000 A^{0}$. Light of wavelength $4000 A^{0}$ is incident on it. The maximum KE of photo-electrons emitted is [given $hc= 2 \times 10^{-25} Jm$]

  1. $3.1 eV$

  2. $2.48 eV$

  3. $0.62 eV$

  4. $5. 58 eV$


Correct Option: C
Explanation:

$K _{max}\ =\ \dfrac{hc}{\lambda}-\dfrac{hc}{\lambda _{0}}$

            $=\dfrac{20\times 10^{-26}}{4\times 10^{-7}}-\dfrac{20\times 10^{-26}}{5\times 10^{-7}}$

           $=\ 20\times 10^{-19}\left ( \dfrac{1}{4} -\dfrac{1}{5}\right )\ J$

          $=10^{-19}J=\dfrac{10^{-19}}{1.6\times 10^{-19}}eV=0.62eV$

So, the answer is option (C).

An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at 0.40$A^{0}$. Then the maximum energy of the photon of the emitted radiation. 

($h = 6.63 \times10^{-34}Js$ and $c= 3 \times10^{8}$ m/s)

  1. $4.9725\times 10^{-15}J$

  2. $6.28\times 10^{-15}J$

  3. $3.15\times 10^{-15}J$

  4. $2.98\times 10^{-15}J$


Correct Option: A
Explanation:

$\lambda _{cutoff} =\ \dfrac{hc}{E}$

$E _{max}=\ \dfrac{20\times 10^{-26}}{0.4\times 10^{-10}}$

$=\ 4.9725\times 10^{-15}\ J$

So, the answer is option (A).

The work function of a certian metal is 2.3 eV .If light of wave number $2\times10^{6}m^{-1}$ falls on it,the kinetic energies of fastest and slowest ejected electorn will be respectively:

  1. 2.48eV ,0.18eV

  2. 0.18eV,Zero

  3. 2.30eV,Zero

  4. 0.18eV,0.18eV


Correct Option: B
Explanation:

$\phi _{ _0}=2.3eV$ 


$\lambda^{-1}=2\times10^6m^{-1}$


Some electrons, although get loosened due to the incident rays, remain stationary.
$\therefore KE _{min}=0$ always

$KE _{max}=TE-\phi _{ _0}$  where TE is the energy of the rays.

$TE=hc\lambda^{-1}$  in Joules

$TE=\dfrac{hc\lambda^{-1}}e$ $in$ $eV$ where e is the charge of one electron

$\therefore TE=\dfrac{6.63\times10^{-34}\times{3\times10^8}\times2\times 10^6}{1.6\times10^{-19}}=2.48eV$

$\therefore KE _{max}=2.48-2.3=0.18eV$

The ratio of momentum  of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of 100 V is

  1. 1

  2. $\displaystyle \sqrt{\frac{2m _e}{m _\alpha}}$

  3. $\displaystyle \sqrt{\frac{m _e}{m _\alpha}}$

  4. $\displaystyle \sqrt{\frac{m _e}{2m _\alpha}}$


Correct Option: C
Explanation:

Since both particles are accelerated by same potential difference, their kinetic energies are equal.

Thus $\dfrac{1}{2}m _{e}v _e^2=\dfrac{1}{2}m _{\alpha}v _{\alpha}^2$
$\implies \dfrac{v _e}{v _{\alpha}}=\sqrt{\dfrac{m _{\alpha}}{m _e}}$
Thus the ratio of their momenta=$\dfrac{m _ev _e}{m _{\alpha}v _{\alpha}}=\sqrt{\dfrac{m _e}{m _{\alpha}}}$
Hence correct answer is option C.

Which one of the following branch of physics deals the impossibility of making simultaneous, arbitrarily precise measurements of the momentum and the position of an electron.

  1. thermodynamics

  2. quantum mechanics

  3. classical electrodynamics

  4. special relativity

  5. general relativity


Correct Option: B
Explanation:

Heisenberg's Uncertainty Principle, as a part of quantum mechanics, theorizes that the position and momentum of an electron cannot be measured precisely at the same time, that is, there is a minimum associated natural error in measurement of the two simultaneously. 

The error in measurement of the two is quantified as $\Delta x.\Delta p\geq\dfrac{\hbar}{2}$

In photoelectric effect, initially when energy of electrons emitted is $E _{0}$, de-Broglie wavelength associated with them is $\lambda _{0}$. Now, energy is doubled then associated de-Broglie wavelength $\lambda^{'}$ is

  1. $\displaystyle\lambda^{'}=\frac{\lambda _{0}}{\sqrt{2}}$

  2. $\displaystyle\lambda^{'}=\sqrt{2}\lambda _{0}$

  3. $\displaystyle\lambda^{'}=\lambda _{0}$

  4. $\displaystyle\lambda^{'}=\frac{\lambda _{0}}{2}$


Correct Option: A
Explanation:

de-Brogile wavelength is given by
$\displaystyle\lambda =\frac{h}{p}$, where h= Planck's constant and p= momentum
Also energy (E) and momentum are related as 
$\displaystyle E =\frac{p^{2}}{2m}$
$\displaystyle \therefore p=\sqrt{2mE}$
$\displaystyle \therefore \lambda =\frac{h}{\sqrt{2mE}}\times \frac{1}{\sqrt{E}}$ as h and m are constants
Hence, $\displaystyle \frac{\lambda _{0}}{{\lambda}'}=\sqrt{\frac{{E}'}{E}}=\sqrt{\frac{2E}{E}}=\sqrt{2}$
$\displaystyle \therefore  {\lambda}'= \frac{\lambda _{0}}{\sqrt{2}}$

When the momentum of a photon is changed by an amount $p'$ then the corresponding change in the de-Broglie wavelength is found to be $0.20$%. Then, the original momentum of the photon was

  1. $300 p'$

  2. $500 p'$

  3. $400 p'$

  4. $100 p'$


Correct Option: B
Explanation:
As, we know de-Broglie wavelength,
$\lambda = \dfrac{h}{p}$
$\therefore \lambda \propto \dfrac{1}{p}$
$\Rightarrow \dfrac{\Delta p}{p} = - \dfrac{\Delta \lambda}{\lambda} \therefore \left| \dfrac{\Delta p}{p} \right | = \left| \dfrac{\Delta \lambda}{\lambda} \right |$
$\Rightarrow \dfrac{p'}{p} = \dfrac{0.20}{100} = \dfrac{1}{500}$
or, $p = 500 p'$

In a photo electric effect experiment, the maximum kinetic energy of the emitted electrons is $1eV$ for incoming radiation of frequency $v _{0}$ and $3eV$ for incoming radiation of frequency $3v _{0}/2$. What is the maximum kinetic energy of the electrons emitted for incoming radiations of frequency $9v _{0}/4$?

  1. $3\ eV$

  2. $4.5\ eV$

  3. $6\ eV$

  4. $9\ eV$


Correct Option: C
Explanation:

$(KE) _{max} = hv - \phi _{0}$
So, $1\ eV = hv _{0} - \phi _{0} .... (i)$
and $3\ eV = \dfrac {hv _{0}}{2} - \phi _{0} .... (ii)$
$\Rightarrow 3\ eV - 1\ eV = \dfrac {hv _{0}}{2}$
or $hv _{0} = 4\ eV$
From Eq. (i), $\phi _{0} = hv _{0} - 1\ eV$
$= 4\ eV - 1\ eV = 3\ eV$
$\therefore (KE) _{mas} = h\times \dfrac {9v _{0}}{4} - 3\ eV$
$= \dfrac {9}{4} (4\ eV) - 3\ eV = 6\ eV$.

Light of wavelength $\lambda$ strikes a photo sensitive surface and electrons are ejected with kinetic energy $E$. If the kinetic energy is to be increased to $2E$, then the wavelength must be changed to $\lambda'$, where :

  1. $\lambda' > \lambda$

  2. $\lambda' = \dfrac {\lambda}{2}$

  3. $\lambda' = 2\lambda$

  4. $\dfrac {\lambda}{2} > \lambda' > \lambda$


Correct Option: D
Explanation:

We have, $E _{k} = \dfrac {hc}{\lambda} - \phi _{0}$


and $2E _{k} = \dfrac {hc}{\lambda'} - \phi _{0}$

By the two relations, we have

$\lambda' > \dfrac {\lambda}{2}$

and $\lambda' < \lambda$

So, $\dfrac {\lambda}{2} < \lambda' < \lambda$.

A photo-cell is illuminated by a source of light, which is placed at a distance $d$ from the cell. If the distance become $d/2$, then number of electrons emitted per second will be : 

  1. Remain same

  2. Four times

  3. Two times

  4. One-fourth


Correct Option: D
Explanation:

Intensity, $I=\dfrac { E }{ At } \ $


where E is the total energy of source,


A is area of illuminated surface,

t is time

$\therefore I=\dfrac { E }{ 4\pi { { { r }^{ 2 } }t } } \\ \dfrac { { I } _{ 1 } }{ { I } _{ 2 } } =\dfrac { E }{ 4\pi { { { r } _{ 1 }^{ 2 } }t } } \times \dfrac { 4\pi { { { r } _{ 2 }^{ 2 } }t } }{ E } \\ =\dfrac { { r } _{ 2 }^{ 2 } }{ { r } _{ 1 }^{ 2 } } \\ \dfrac { { I } _{ 1 } }{ { I } _{ 2 } } =\dfrac { 4 }{ 1 } \\ \Rightarrow \dfrac { { I } _{ 2 } }{ { I } _{ 1 } } =\dfrac { 1 }{ 4 } $

Since, $\propto$ number of photoelectrons emitted

Therefore, Number of electrons emitted is a quarter of the initial number.

The formula for kinetic mass of photon is:
where $h$ is Planck's constant and $v,\lambda, c$ are frequency, wavelength and speed of photon respectively.

  1. $\cfrac { hv }{ \lambda } $

  2. $\cfrac { h }{ c\lambda } $

  3. $\cfrac { hv }{ c } $

  4. $\cfrac { h\lambda }{ c } $


Correct Option: B
Explanation:

Energy of the photon is given by,

$E=hv=\dfrac{hc}{\lambda}$,  ...(1)
also for particle of zero mass,
$E=mc^2$,   ...(2)
form eq(1) and (2) we get,
$mc^2=\dfrac{hc}{\lambda}$
$\therefore$ kinetic mass of photon$= m=\dfrac{h}{c\lambda}$

If momentum of a photon of an electromagnetic radiation is $3.3\times 10^{-29}$ kg m/sec, then frequency of associated wave is:

  1. $3.0\times 10^3Hz$

  2. $6.0\times 10^3Hz$

  3. $7.5\times 10^5Hz$

  4. $1.5\times 10^{13}Hz$


Correct Option: D
Explanation:

$p=\dfrac {hv}{c}$
$\Rightarrow v=\dfrac {cp}{h}=\dfrac {(3\times 20^8)\times (3\cdot 3\times 10{-29})}{6\cdot 6\times 10^{-34}}$


$=1\cdot 5\times 10^{13}Hz.$

Assume that a neutron breaks into a proton and an electron. The energy released suring this process is (mass of neutron $= 1.6725 \times 10^{-27} kg,$
mass od proton $= 1.6725 \times 10^{-27} kg,$ mass of electron$= 9 \times 10^{-31}kg)$

  1. 0.73 MeV

  2. 7.10 MeV

  3. 6.30 MeV

  4. 5.4 MeV


Correct Option: A
Explanation:

$\triangle m = (m _P + m _e) -m _n$

        $= 9 \times 10^{-31} kg $
 $(mc^2) \space energy \space released = (9 \times 10^{-31} kg) c^2 \space joules$
$= \dfrac{9 \times 10^{-31} \times (3 \times 10^8 )^2}{1.6 \times 10^{-13}} Mev$

$= 0.73 Mev$
Hence option (A) is correct

A monochromatic source of light is placed at a large distance $d$ from a metal surface. Photoelectrons are ejected at rate $n$, the kinetic energy being $E$. If the source is brought nearer to distance $d/2$, the rate and kinetic energy per photoelectron become nearly :

  1. 2n and 2E

  2. 4n and 4E

  3. 4n and E

  4. n and 4E


Correct Option: C
Explanation:

The rate is inversely proportional to square of the distance: $n\propto \dfrac{1}{{r}^{2}}$


So the new rate will be $4n$

Kinetic energy is not related to the distance, hence it will remain same $E$.

The work function of a certain metal is $3.31 \, \times \,  10^{-19} J.$ Then, the maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength 5000 A is
$(Given\, h  = 6.62\times10^{-34} J-s, \, c= 3\times10^{-8} \, ms^{-1},\, e=  1.6 \times10^{-19} \, C)$

  1. $248 eV$

  2. $0.41 eV$

  3. $2.07 eV$

  4. $0.82 eV$


Correct Option: B
Explanation:

Work function $W _0 \, = \, 3.31 \, \times \, 10^{-19} \, J$
Wavelength of incident radiation
 $\lambda \, = \, 5000 \, \times \, 10^{-10} \, m$
$E \, = \, W _0 \, + \, KE$
(According to Einstein equation)
$\displaystyle \frac{hc}{\lambda} \, 3.31 \, \times \, 10^{-19} \, + \, KE$
$KE \, = \, - \, 3.31 \, \times \, 10^{-19} + \, \displaystyle \frac{6.62 \, \times \, 10^{-34} \, \times \, 3 \, \times \, 10^8}{5000 \, \times \, 10^{10}}$
$= \, - \, 3.31 \, \times \, 10^{-19} \, + \, 10^{-19} \, + \, \displaystyle \frac{6.62 \, \times \, 3}{5} \, \times \, 10^{-19}$
$= \, (- \, 3.31 \, \times \, 1.324 \, \times \, 3) \, \times \, 10^{-19}$
$= \, (3.972 \, - \, 3.31) \, \times \, 10^{-19} \, = \, 0.662 \, \times \, 10^{-19} \, J$
$\Rightarrow \, E \, = \, \displaystyle \frac{0.662 \, \times \, 10^{19}}{1.6 \, \times \, 10^{-19}} \, = \, 0.41 eV$

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